Question 19 4 points Save The probability that a standard normal random variable

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  Question 19 4 points   Save   The probability that a standard normal random variable, Z, falls between -2.00 and -0.44 is 0.6472. True Flase The probability that a standard normal random variable, Z, falls between -2.00 and -0.44 is 0.6472. Any set of normally distributed data can be transformed to its standardized form. The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above what weight (in pounds) do 89.80% of the weights occur? For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. The value of Z is The probability that a standard normal random variable, Z, falls between - 1.50 and 0.81 is 0.7242. True or False: A normal probability plot may be used to assess the assumption of normality for a particular batch of data. A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants.

Explanation / Answer

(19)Flase

(20)True

(21) P(X>c)= 0.898

--> P((X-mean)/s <(c-3.2)/0.8) =1-0.898 =0.102

--> P(Z<(c-3.2)/0.8) =0.102

--> (c-3.2)/0.8 =1.27 (from standard normal table)

--> c =3.2-1.27*0.8 =2.184

(22)1.16

(23)True

(24)True

(25) P(X<c)=0.86

--> P(Z<(c-68)/3.5)=0.86

--> (c-68)/3.5 =1.08 (from standard normal table)

--> c= 68+1.08*3.5 =71.78

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